More on The Dragon Fractal

Earlier I wrote about a program implementing the algorithm for the Dragon fractal. Lest it appear that this is really complicated, I wanted to give some information about the process.

You can do this very easily with straw paper or a long piece of thin paper. Of course, paper will keep the iterations very low since a limited number of folds are possible. If you start with the paper flat, then fold right, then fold right, then fold right… then begin unfolding half at a time, you will generate the pattern. That’s one of the fun things about this pattern. It folds in on itself.

Folding left repeatedly would generate the same thing, only in reverse rotation.

If you tried to get down to the actual turns (based on right rotation) in the paper, you would find an interesting pattern:

  • starting paper
  • paper with bend to the right in the middle (R)
  • paper with two right bends and a left bend. (RRL)
  • paper with two right bends and a left bend, followed by two more right bends and two left bends. (RRLRRLL)
  • RRLRRLLRRRLLRLL
  • RRLRRLLRRRLLRLLRRRLRRLLLRRLLRLL

The pattern that appears for each iteration amounts to the following:

  1. perform all the turns of the previous iteration.
  2. perform a RIGHT turn.
  3. perform all the turns of the previous iteration in reverse order, replacing LEFT with RIGHT and RIGHT with LEFT.

It is not overly complicated, but yields interesting results.

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About George

I'm interested in theology, languages, translation and various sorts of fermentation.
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